What you care about most

1. Unique visitors. These are real people visiting the site.
2. Number of Visits. That's the number of times the Uniques visitors came to the site.
3. Pages. The number of pages these visitors actually looked at.

Other important stats:

Visit duration. This is how long the visitors stay on the site. Longer is usually better, but it really depends on what you offer. What does duration mean? Hard to say, they may simply be getting to what they want quickly, or they may not be getting to it at all and leaving, or maybe all they were looking for was your contact information?

Pages being Viewed
What pages are they actually viewing? I look at 2 things here
A) which are they viewing the most, and are those the pages I want them viewing,
B) Which pages are not being viewed (click to view the whole list). This tells you something important as well, it may be a hidden page or a page you are no longer using, or it may be a page there are no obvious links to that you want people to view. In any case, it helps you see what you need to do, like perhaps adding more links to pages you want to draw attention to or removing an old outdated page.

Look at other things in this list. Pages that show up as numbered, e.g., page62.html are pages that you have links to, but have not added an "alias" for in {SETTINGS}. Adding an alias to pages will help with search optimization as well as making it easier to see what page is being viewed in the stats. For more on accessing Page Settings, click the Page Settings link in the left column.

The point is, you can also use your stats to find things that are incorrect or get "broken" and remedy the situation.

Connect to site from:
This tells you from what external sites people came to you. Sometimes it's useful, often not, but interesting to look at as someone may post a link to you on a blog, or mention it in another online publication, or you can check affiliates to see if you are really getting any traffic directly from them or not. If not, and you should be, you may want to contact them and see how to get more visibility, conversely, you may find a site that has a link to you that you do not want to be affiliated with. In either case, you want to know.

Search Keyphrases and Search Keywords
View the full list each month. These are the actual terms and phrases that people are using to search Google, Yahoo, Ask, MSN etc. and ending up at your site. These search terms match content or SEO information embedded in your pages...somewhere. Are there good terms way down the list? if so, maybe you can add some additional text to your pages using those terms, words or phrases. Are there words, terms of phrases that you would expect to see there that are not? This might indicate that you are not using them in the text of your site, or that you are not using them enough, or that you haven't completed your SEO information for a particular page.